Question
Ena spends all her income on her rent,travel and life expenses. She spends third of her income on rent,fifth of her income on travel ans 420$ on living expenses. How much does she make per month?
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Answer to a math question Ena spends all her income on her rent,travel and life expenses. She spends third of her income on rent,fifth of her income on travel ans 420$ on living expenses. How much does she make per month?
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4.8113 Answers
1. Denote Ena's monthly income by \( x \).
2. She spends one-third on rent:
\frac{x}{3}
3. She spends one-fifth on travel:
\frac{x}{5}
4. Total expenses on rent, travel, and living expenses:
\frac{x}{3} + \frac{x}{5} + 420
5. The total expenses are equals to her monthly income:
\frac{x}{3} + \frac{x}{5} + 420 = x
6. Find a common denominator for fractions:
\frac{5x}{15} + \frac{3x}{15} + 420 = x
7. Combine the fractions:
\frac{8x}{15} + 420 = x
8. Isolate \( x \) by moving \( \frac{8x}{15} \) to the right:
420 = x - \frac{8x}{15}
9. Simplify the right side:
420 = \frac{15x - 8x}{15}
10. Combine like terms:
420 = \frac{7x}{15}
11. Multiply both sides by 15:
420 \cdot 15 = 7x
12. Simplify:
6300 = 7x
13. Divide both sides by 7 to find \( x \):
x = \frac{6300}{7}
14. Simplify:
x = 900
2. She spends one-third on rent:
3. She spends one-fifth on travel:
4. Total expenses on rent, travel, and living expenses:
5. The total expenses are equals to her monthly income:
6. Find a common denominator for fractions:
7. Combine the fractions:
8. Isolate \( x \) by moving \( \frac{8x}{15} \) to the right:
9. Simplify the right side:
10. Combine like terms:
11. Multiply both sides by 15:
12. Simplify:
13. Divide both sides by 7 to find \( x \):
14. Simplify:
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